Finite Group Databasebeta

← C₂²×C₃×C₂₅ #64469

Subgroups — C₂²×C₃×C₂₅ #64469

Order 300.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₅	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₅	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃×C₅	C₅	1	1	yes	maximal, characteristic
5	C₂×C₂₅	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₅	C₂×C₅	1	3	yes	—
7	C₂₅	C₂²×C₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₂²×C₅	C₃×C₅	1	1	yes	characteristic
9	C₃×C₅	C₂²×C₅	1	1	yes	characteristic
10	C₂²×C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅	C₂×C₃×C₅	1	3	yes	—
12	C₂×C₃	C₂×C₂₅	1	3	yes	direct product factor
13	C₅	C₂²×C₃×C₅	1	1	yes	characteristic
14	C₂²	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
15	C₃	C₂²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₃×C₂₅	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₂₅	C₂	direct (N × H)
2. C₂²×C₂₅	C₃	direct (N × H)
3. C₃×C₂₅	C₂²	direct (N × H)
5. C₂×C₂₅	C₂×C₃	direct (N × H)
7. C₂₅	C₂²×C₃	direct (N × H)
10. C₂²×C₃	C₂₅	direct (N × H)
12. C₂×C₃	C₂×C₂₅	direct (N × H)
14. C₂²	C₃×C₂₅	direct (N × H)
15. C₃	C₂²×C₂₅	direct (N × H)
16. C₂	C₂×C₃×C₂₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₂₅	2
C₂²×C₂₅	3
C₂²×C₃×C₅	5